The word 'that'

English as a Second Language English Vocabulary, Grammar and Idioms
1

I’d like to know if there are rules for using/not using the word ‘that’.

For example:

She told me that she was pregnant.

vs

She told me she was pregnant.

I didn’t know that you were at the party.

vs

I didn’t know you were at the party.

Thanks!

2

There are numerous uses for the word ‘that’ so I will only explain based on the examples you’ve given.
In this case, the word ‘that’ is a conjunction used to connect two clauses. Note that both constructions are correct, even if they do or do not have this word. In spoken English, ‘that’ is often omitted in order to pronounce and express the idea more rapidly, especially if the verb used in the ‘that’ clause is very common (e.g. to be in “She told me she was pregnant”). You can also skip this word in articles or essays if your writing will gain a weird sonority because of the repetition.